SciELO - Scientific Electronic Library Online

vol.13 issue1Pattern Recognition for Micro Workpieces ManufacturingUsing Simulated Annealing with a Neighborhood Heuristic for Roll Cutting Optimization author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • Have no similar articlesSimilars in SciELO


Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.13 n.1 México Jul./Sep. 2009




G'3–Stable Semantics and Inconsistency


Semantica G3 '–Estable e Inconsistencia


Mauricio Osorio1, Claudia Zepeda2, Juan Carlos Nieves3 and José Luis Carballido2


1 Universidad de las Américas – Puebla, CENTIA Email:

2 Benemérita Universidad Autónoma de Puebla Facultad de Ciencias de la Computación Email: ,

3 Universitat Politècnica de Catalunya Software Department (LSI) Email:


Article received on July 19, 2008
Accepted on April 03, 2009



We present an overview on how to perform non–monotonic reasoning based on paraconsistent logics. In particular, we show that one can define a logic programming semantics based on the paraconsistent logic G'3 which is called G'3–stable semantics. This semantics defines a frame for performing non–monotonic reasoning in domains which are pervaded with vagueness and inconsistencies. In fact, we show that, by considering also a possibilistic logic point of view, one can use this extended framework for defining a possibilistic logic programming approach able to deal with reasoning, which is at the same time non–monotonic and uncertain.

Keywords: G'3–stable semantics, Logic Programming, Non–Monotonic Reasoning.



Presentamos un resumen acerca de cómo realizar razonamiento no–monótono basado en lógicas paraconsistentes. En particular, mostramos que es posible definir una semántica de programación lógica basada en la lógica paraconsistente G'3, la cual es llamada semántica G'3–estable. Esta semántica define un marco para realizar razonamiento no–monótono en dominios los cuales están plagados de vaguedades e inconsistencias. De hecho, mostramos que al considerar también un punto de vista lógico posibilista, es posible usar la extensión de este marco de trabajo para definir un enfoque de programación lógica posibilístico que puede tratar con razonamiento que es al mismo tiempo no monótono e incierto.

Palabras Clave: Semántica : G'3–estable, Programación lógica, Razonamiento No–Monótono.





We are grateful to anonymous referees for their useful comments.



1. Baral C., Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge, 2003        [ Links ]

2. Bench–Capon T. J. M. and Dunne P. E., Argumentation in artificial intelligence. Artificial Intelligence, 171 (10–15): 619–641 (2007).        [ Links ]

3. Béziau J., Paraconsistent logic from a modal viewpoint. Journal of Applied Logic, 3:7–14 (2005).        [ Links ]

4. Carballido J. L., Nieves J. C., and Osorio M., Inferring Preferred Extensions by Pstable Semantics. Iberoamerican Journal of Artificial Intelligence (Inteligencia Artificial), 13(41): 38–53 (2009).        [ Links ]

5. Carnielli W. A., Coniglio M., and Marcos J., Logics of formal inconsistency. Handbook of Philosophical Logic, 14:(15–107), Springer, 2007.        [ Links ]

6. da Costa N. C. A., On the theory of inconsistent formal systems (in Portuguese). PhD thesis, UFPR Curitiva, 1963.        [ Links ]

7. de Amo S., Carnielli W. A., and Marcos J., Formal inconsistency and evolutionary databases. Logic and Logical Philosophy, 8(1): 115–152 (2000).        [ Links ]

8. de Amo S., Carnielli W. A., and Marcos J., A logical framework for integrating inconsistent information in multiple databases. Paper presented at FOIKS, Vol.2284 of Lecture Notes in Computer Science, Springer, 2002, 67–84.        [ Links ]

9. Donini F. M., Nardi D., and Rosati R., Ground nonmonotonic modal logics. Logic and Computation, 7(4) (1997).        [ Links ]

10. Dubois D., Lang J., and Prade H., Possibilistic logic. In D. Gabbay, C. J. Hogger, and J. A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 3 of Nonmonotonic Reasoning and Uncertain Reasoning, Oxford University Press, 1994, 439–513.        [ Links ]

11. Gelfond M. and Lifschitz V., The Stable Model Semantics for Logic Programming. In Kowalski R. and Bowen K., editors. Paper presented at 5th Conference on Logic Programming, MIT Press, 1988, 1070–1080.        [ Links ]

12. Gelfond M. and Lifschitz V., Logic Programs with Classical Negation. In D. Warren and P. Szeredi, Editors. Paper presented at 7th Int. Conf. on Logic Programming, Jerusalem, Israel, MIT Press, 1990, 579–597.        [ Links ]

13. Konolige K., On the relation between default and autoepistemic logic. In M. L. Ginsberg, editor, Readings in Nonmonotonic Reasoning,. Kaufmann, Los Altos, CA, 1987, 195–226.        [ Links ]

14. López A., Implementing pstable. Paper presented at LoLaCOM, CEUR Vol 220, on line:–WS/Vol–220/, Apizaco, Tlaxcala, 2006.        [ Links ]

15. McDermott D., Nonmonotonic logic II: Nonmonotonic modal theories. ACM Transactions on Computer Systems, 29: 33–57 (1982).        [ Links ]

16. McDermott D. and Doyle J., Non–monotonic logic I. Artificial Intelligence, 13:41–72 (1980).        [ Links ]

17. Mendelson E., Introduction to Mathematical Logic. Wadsworth, Belmont, CA, third edition, 1987.        [ Links ]

18. Minsky M., A framework for representing knowledge. In P. Winston, editor, The Psychology of Computer Vision, Mcgraw–Hill, New York, 1975.        [ Links ]

19. Nicolas P., Garcia L., Stéphan I., and Lafèvre C., Possibilistic Uncertainty Handling for Answer Set Programming. Annal of Mathematics and Artificial Intelligence, 47(1–2): 139–181 (2006).        [ Links ]

20. Nieves J. C., Modeling arguments and uncertain information — A non–monotonic reasoning approach. PhD thesis, Software Department (LSI), Technical University of Catalonia, 2008.        [ Links ]

21. Nieves J. C., Osorio M., and Cortés U., Semantics for possibilistic disjunctive programs. In S. Costantini and R. Watson, editors. Paper presented at Answer Set Programming: Advances in Theory and Implementation (ICLP–07 Workshop), 2007, 271–284.        [ Links ]

22. J. C. Nieves, M. Osorio, and U. Cortés., Preferred extensions as stable models. Theory and Practice of Logic Programming (TPLP), 8(4):527–543 (2008).        [ Links ]

23. Osorio M., Arrazola J. R., and Carballido J. L., Logical Weak Completions of Paraconsistent Logics. Journal of Logic and Computation, doi: 10.1093/log–com/exn015 (2008).        [ Links ]

24. Osorio M. and Carballido J., Brief study of G'3 logic. Journal of Applied Non–Classical Logics, 18(4):475–499 (2008).        [ Links ]

25. Osorio M. and Navarro J. A., Modal logic S52 and FOUR (abstract). In Proceedings of Annual Meeting of the Association for Symbolic Logic, 2003.        [ Links ]

26. Osorio M., Navarro J. A., Arrazola J., and Borja V., Ground nonmonotonic modal logic S5: New results. Journal of Logic and Computation, 15(5):787–813 (2005).        [ Links ]

27. Osorio M., Navarro J. A., Arrazola J. R., and Borja V., Logics with Common Weak Completions. Journal of Logic and Computation, 16(6):867–890 (2006).        [ Links ]

28. Osorio M. and Zepeda C., Update sequences based on minimal generalized pstable models. Paper presented at MICAI 2007: Advances in Artificial Intelligence, 6th Mexican International Conference on Artificial Intelligence, Vol. 4827 of Lecture Notes in Computer Science, Springer, 2007, 283–293.        [ Links ]

29. Osorio M. and. Zepeda C., Pstable theories and preferences. In Electronic Proceedings of the 18th International Conference on Electronics, Communications, and Computers (CONIELECOMP 2008), March, 2008.        [ Links ]

30. Pearce D., Stable inference as intuitionistic validity. Journal of Logic Programming, 38, 79–91 (1999).        [ Links ]

31. Sakama C. and Inoue K., Paraconsistent stable semantics for extended disjunctive programs. Journal of Logic and Computation, 5:265–285 (1995).        [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License